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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On Lakshmikantham's comparison for ordinary differential equations


Author: Giovanni Vidossich
Journal: Proc. Amer. Math. Soc. 53 (1975), 412-414
MSC: Primary 34G05
MathSciNet review: 0390421
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Abstract: The paper describes the relation between Lakshmikantham's comparison and other known facts.


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  • [1] Ronald Becker and Giovanni Vidossich, Some applications of a simple criterion for the existence of periodic solutions of ordinary differential equations, J. Math. Anal. Appl. 48 (1974), 51–60. MR 0350119 (50 #2612)
  • [2] R. Conti and G. Sansone, Equazioni differenziali nonlineari, Edizioni Cremonese, Rome, 1956; English transl., Internat. Ser. of Monographs in Pure and Appl. Math., vol. 67, Macmillan, New York, 1964. MR 19, 547; 31 #1417.
  • [3] G. E. Ladas and V. Lakshmikantham, Differential equations in abstract spaces, Academic Press, New York-London, 1972. Mathematics in Science and Engineering, Vol. 85. MR 0460832 (57 #824)
  • [4] V. Lakshmikantham, Notes on a variety of problems of differential systems, Arch. Rational Mech. Anal. 10 (1962), 119–126. MR 0141840 (25 #5237)
  • [5] V. Lakshmikantham and S. Leela, Differential and integral inequalities, vols. I, II, Academic Press, New York, 1969.
  • [6] G. Vidossich, Existence, comparison and asymptotic behavior of solutions of ordinary differential equations in finite and infinite dimensional Banach spaces, Notas de Matemática, no. 24, Universidade de Brasília, 1972.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0390421-3
PII: S 0002-9939(1975)0390421-3
Keywords: Lakshmikantham comparison, pairing comparison, stability theorem
Article copyright: © Copyright 1975 American Mathematical Society